A112967 Sum(Omega(i)*Omega(j): i+j=n), with Omega=A001222.

0, 0, 0, 1, 2, 5, 6, 10, 10, 17, 18, 26, 24, 33, 30, 41, 38, 52, 46, 64, 54, 71, 62, 87, 70, 91, 80, 106, 90, 116, 100, 130, 112, 139, 120, 163, 130, 161, 144, 185, 152, 190, 162, 208, 172, 205, 178, 244, 186, 232, 208, 262, 212, 267, 218, 291, 246, 287, 248, 329, 252

Offset: 1

Author

Reinhard Zumkeller, Oct 07 2005

Keywords

• nonn
• look

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A112965, A112968, A022559.

Programs

Maple

X:= Vector(100, numtheory:-bigomega):
seq(add(X[i]*X[n-i],i=1..n-1),n=1..100); # Robert Israel, Mar 15 2017

Mathematica

Table[Sum[PrimeOmega[i] PrimeOmega[n - i],{i,1, n - 1} ], {n, 1, 61}] (* Indranil Ghosh, Mar 16 2017 *)

PARI

for(n=1, 61, print1(sum(i=1, n - 1, bigomega(i) * bigomega(n - i)),", ")) \\ Indranil Ghosh, Mar 16 2017

Formula

G.f.: (Sum_{p prime, k>=1} x^(p^k)/(1 - x^(p^k)))^2. - Ilya Gutkovskiy, Mar 15 2017